

A244056


Maximum score achievable in the 2048 game on an n X n grid.


0



0, 180, 16352, 3932100, 3221225376, 9620726742900, 108086391056891712, 4648579506574807006980, 773712524553362671811952320, 501989637690378842992694469328500, 1276058875953519237987654777869130792480, 12756026253559516436958430851954862781420797380
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OFFSET

1,2


COMMENTS

This sequence is based on the original 2048 game by G. Cirulli, scores are given as follows:
. combining together two 2^(k1) tiles, to form a 2^k tile, you get (k1)*2^k points;
. nine times out of ten you get a [2] new tile on the board, while, one time out of ten, appears a [4] tile.


LINKS

Table of n, a(n) for n=1..12.
M. Ripà, 2048 game: massimo punteggio, matematicamente.it, June 2014 (in Italian).


FORMULA

a(n) = 4*(n^21)*(2^n^21).


EXAMPLE

For n=4, the maximum score you can achieve with a perfect game is a(4)=3932100. You can get it less than one out of 10^6011 (perfect) games played.


CROSSREFS

Sequence in context: A287022 A217791 A035830 * A091033 A146530 A057867
Adjacent sequences: A244053 A244054 A244055 * A244057 A244058 A244059


KEYWORD

nonn,easy


AUTHOR

Marco Ripà, Jun 18 2014


EXTENSIONS

a(12) corrected by Colin Barker, Jun 18 2014


STATUS

approved



